Problem: Solve for $x$ and $y$ using elimination. ${5x+y = 7}$ ${4x-y = 2}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $9x = 9$ $\dfrac{9x}{{9}} = \dfrac{9}{{9}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {5x+y = 7}\thinspace$ to find $y$ ${5}{(1)}{ + y = 7}$ $5+y = 7$ $5{-5} + y = 7{-5}$ ${y = 2}$ You can also plug ${x = 1}$ into $\thinspace {4x-y = 2}\thinspace$ and get the same answer for $y$ : ${4}{(1)}{ - y = 2}$ ${y = 2}$